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Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux. (English) Zbl 0619.76091
The artificial viscosity (Q) method of von Neumann and Richtmyer is a tremendously useful numerical technique for following shocks wherever and whenever they appear in the flow. We show that it must be used with some caution, however, as serious Q-induced errors (on the order of 100 %) can occur in some strong shock calculations. We investigate three types of Q errors: 1. Excess Q heating, of which there are two types: (a) excess wall heating on shock formation and (b) shockless Q heating; 2. Q errors when shocks are propagated over a nonuniform mesh; and 3. Q errors in propagating shocks in spherical geometry.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
65Z05 Applications to the sciences
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